Question

An octagon has three equal angles each of measure 115.if all the remaining angles have equal measure find the measure of each of these remaining angles?

Answer 1

Step-by-step explanation:

Sum of measure of angles of polygon is calculated by the formula,

sum = (n - 2) × 180° where n is the number of sides.

For an octagon,

n = 8

Therefore,

sum of all angles = (8 - 2)×180°

= 6 × 180°

= 1080°

Given,

the octagon has three angles of 115° each.

Sum of three angle = 115 × 3

= 345°

Now, there are 5 remaining angles. It is given that these remaining angles are equal.

So, Let the measure of one angle be x.

Then,

Measure of remaining 5 angles = 5x

We have already calculated the sum of all angles.

Therefore,

5x + 345° = 1080°

5x = 735°

x = 147°

Therefore, each of the remaining angles have a measure of 147°.

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